知道起点和距离计算第二个点 [英] Calculate second point knowing the starting point and distance

问题描述

使用纬度和经度值(A 点)，我试图计算另一个 B 点，距离 A 点 X 米，距离为 0 弧度.然后显示 B 点的纬度和经度值.

using a Latitude and Longitude value (Point A), I am trying to calculate another Point B, X meters away bearing 0 radians from point A. Then display the point B Latitude and Longitude values.

示例(伪代码):

PointA_Lat = x.xxxx;
PointA_Lng = x.xxxx;
Distance = 3; //Meters
bearing = 0; //radians

new_PointB = PointA-Distance;

我能够计算出两点之间的距离，但我想找到的是知道距离和方位的第二个点.

I was able to calculate the distance between two Points but what I want to find is the second point knowing the distance and bearing.

最好使用 PHP 或 Javascript.

Preferably in PHP or Javascript.

谢谢

推荐答案

您似乎正在以米为单位测量距离 (R)，并从正东逆时针方向 (theta).对于您的目的(数百米)，平面几何应该足够准确.在这种情况下，

It seems you are measuring distance (R) in meters, and bearing (theta) counterclockwise from due east. And for your purposes (hundereds of meters), plane geometry should be accurate enough. In that case,

dx = R*cos(theta) ; theta measured counterclockwise from due east
dy = R*sin(theta) ; dx, dy same units as R

如果从正北顺时针测量 theta(例如，罗盘方位)，dx 和 dy 的计算略有不同:

If theta is measured clockwise from due north (for example, compass bearings), the calculation for dx and dy is slightly different:

dx = R*sin(theta)  ; theta measured clockwise from due north
dy = R*cos(theta)  ; dx, dy same units as R

无论哪种情况，经度和纬度的变化为:

In either case, the change in degrees longitude and latitude is:

delta_longitude = dx/(111320*cos(latitude))  ; dx, dy in meters
delta_latitude = dy/110540                   ; result in degrees long/lat

常数 110540 和 111320 之间的差异是由于地球的扁率(极地和赤道周长不同).

The difference between the constants 110540 and 111320 is due to the earth's oblateness (polar and equatorial circumferences are different).

这是一个有效的例子，使用了你后面问题中的参数:

Here's a worked example, using the parameters from a later question of yours:

给定起始位置在经度 -87.62788 度，纬度 41.88592 度，求起点西北500米处的坐标.

Given a start location at longitude -87.62788 degrees, latitude 41.88592 degrees, find the coordinates of the point 500 meters northwest from the start location.

如果我们从正东逆时针测量角度，西北"对应到 theta=135 度.R 是 500 米.

If we're measuring angles counterclockwise from due east, "northwest" corresponds to theta=135 degrees. R is 500 meters.

dx = R*cos(theta) 
   = 500 * cos(135 deg) 
   = -353.55 meters

dy = R*sin(theta) 
   = 500 * sin(135 deg) 
   = +353.55 meters

delta_longitude = dx/(111320*cos(latitude)) 
                = -353.55/(111320*cos(41.88592 deg))
                = -.004266 deg (approx -15.36 arcsec)

delta_latitude = dy/110540
               = 353.55/110540
               =  .003198 deg (approx 11.51 arcsec)

Final longitude = start_longitude + delta_longitude
                = -87.62788 - .004266
                = -87.632146

Final latitude = start_latitude + delta_latitude
               = 41.88592 + .003198
               = 41.889118

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